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x 1 2 3 4
f ( x ) 70 40 10 -20

Linear

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x 1 2 3 4
h ( x ) 70 49 34.3 24.01
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x 1 2 3 4
m ( x ) 80 61 42.9 25.61

Neither

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x 1 2 3 4
f ( x ) 10 20 40 80
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x 1 2 3 4
g ( x ) -3.25 2 7.25 12.5

Linear

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For the following exercises, use the compound interest formula, A ( t ) = P ( 1 + r n ) n t .

After a certain number of years, the value of an investment account is represented by the equation 10 , 250 ( 1 + 0.04 12 ) 120 . What is the value of the account?

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What was the initial deposit made to the account in the previous exercise?

$ 10 , 250

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How many years had the account from the previous exercise been accumulating interest?

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An account is opened with an initial deposit of $6,500 and earns 3.6 % interest compounded semi-annually. What will the account be worth in 20 years?

$ 13 , 268.58

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How much more would the account in the previous exercise have been worth if the interest were compounding weekly?

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Solve the compound interest formula for the principal, P .

P = A ( t ) ( 1 + r n ) n t

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Use the formula found in the previous exercise to calculate the initial deposit of an account that is worth $ 14 , 472.74 after earning 5.5 % interest compounded monthly for 5 years. (Round to the nearest dollar.)

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How much more would the account in the previous two exercises be worth if it were earning interest for 5 more years?

$ 4,572.56

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Use properties of rational exponents to solve the compound interest formula for the interest rate, r .

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Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $9,000 and was worth $13,373.53 after 10 years.

4 %

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Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded monthly, had an initial deposit of $5,500, and was worth $38,455 after 30 years.

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For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.

y = 3742 ( e ) 0.75 t

continuous growth; the growth rate is greater than 0.

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y = 2.25 ( e ) 2 t

continuous decay; the growth rate is less than 0.

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Suppose an investment account is opened with an initial deposit of $ 12 , 000 earning 7.2 % interest compounded continuously. How much will the account be worth after 30 years?

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How much less would the account from Exercise 42 be worth after 30 years if it were compounded monthly instead?

$ 669.42

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Numeric

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

f ( x ) = 2 ( 5 ) x , for f ( 3 )

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f ( x ) = 4 2 x + 3 , for f ( 1 )

f ( 1 ) = 4

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f ( x ) = e x , for f ( 3 )

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f ( x ) = 2 e x 1 , for f ( 1 )

f ( 1 ) 0.2707

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f ( x ) = 2.7 ( 4 ) x + 1 + 1.5 , for f ( 2 )

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f ( x ) = 1.2 e 2 x 0.3 , for f ( 3 )

f ( 3 ) 483.8146

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f ( x ) = 3 2 ( 3 ) x + 3 2 , for f ( 2 )

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Technology

For the following exercises, use a graphing calculator to find the equation of an exponential function given the points on the curve.

( 0 , 3 ) and ( 3 , 375 )

y = 3 5 x

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( 3 , 222.62 ) and ( 10 , 77.456 )

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( 20 , 29.495 ) and ( 150 , 730.89 )

y 18 1.025 x

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( 5 , 2.909 ) and ( 13 , 0.005 )

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( 11,310.035 ) and ( 25,356.3652 )

y 0.2 1.95 x

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Extensions

The annual percentage yield (APY) of an investment account is a representation of the actual interest rate earned on a compounding account. It is based on a compounding period of one year. Show that the APY of an account that compounds monthly can be found with the formula APY = ( 1 + r 12 ) 12 1.

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Questions & Answers

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply
Practice Key Terms 4

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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